We compute three-point functions for the $SL(2,\mathbb{R})$-WZNW model. After reviewing the case of the two-point correlator, we compute spectral flow preserving and nonpreserving correlation functions in the space-time picture involving three vertex operators carrying an arbitrary amount of spectral flow. When only one or two insertions have nontrivial spectral flow numbers, the method we employ allows us to find expressions without any constraint on the spin values. Unlike these cases, the same procedure restrains the possible spin configurations when the three vertices belong to nonzero spectral flow sectors. We perform several consistency checks on our results. In particular, we verify that they are in complete agreement with previously computed correlators involving states carrying a single unit of spectral flow.

• Received 11 December 2013

DOI:https://doi.org/10.1103/PhysRevD.89.066006